Energy Systems

, Volume 3, Issue 3, pp 221–258

Optimal power flow: a bibliographic survey I

Formulations and deterministic methods
  • Stephen Frank
  • Ingrida Steponavice
  • Steffen Rebennack
Original Paper

Abstract

Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.

Keywords

Electric power systems Optimal power flow Optimal power flow formulations Optimal power flow requirements Deterministic optimization Global optimization Nonlinear optimization Survey 

Abbreviations

The following summarizes the meanings of abbreviations and acronyms used throughout the paper:

AC

Alternating Current

ASP

Active Set and Penalty

BFGS

Broyden-Fletcher-Goldfarb-Shanno (quasi-Newton method)

CG

Conjugate Gradient

DC

Direct Current

DFP

Davidon-Fletcher-Powell (quasi-Newton method)

ECQ

Extended Conic-Quadratic

HVDC

High-Voltage Direct Current

FACTS

Flexible AC Transmission Systems

GRG

Generalized Reduced Gradient

IPM

Interior Point Method

KKT

Karush-Kuhn-Tucker (conditions for optimality)

LP

Linear Programming

MBAL

Modified Barrier-Augmented Lagrangian

MCC

Multiple Centrality Corrections

MILP

Mixed Integer Linear Programming

MINLP

Mixed Integer-Nonlinear Programming

MW

Megawatt

NC

Nonlinear Complementarity

NLP

Nonlinear Programming

OPF

Optimal Power Flow

ORPF

Optimal Reactive Power Flow

PC

Predictor-Corrector

PD

Primal-Dual

PDIPM

Primal-Dual Interior Point Method

PDLB

Primal-Dual Logarithmic Barrier

QP

Quadratic Programming

RG

Reduced Gradient

SCED

Security-Constrained Economic Dispatch

SCIPM

Step-Controlled Interior Point Method

SCUC

Security-Constrained Unit Commitment

SDP

Semi-Definite Programming

SLP

Sequential Linear Programming

SQP

Sequential Quadratic Programming

TRIPM

Trust Region Interior Point Method

UPFC

Unified Power Flow Controller

VAR

Volt-Ampere Reactive

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Stephen Frank
    • 1
  • Ingrida Steponavice
    • 2
  • Steffen Rebennack
    • 3
  1. 1.Department of Electrical Engineering and Computer ScienceColorado School of MinesGoldenUSA
  2. 2.Department of Mathematical Information TechnologyUniversity of JyvaskylaAgoraFinland
  3. 3.Division of Economics and BusinessColorado School of MinesGoldenUSA

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